Is there a way to work out an unknown waveshaper function, that was used to distort and map the values of an input signal to new output signal, form the output if we only have input signal and the output signal but missing the waveshaper function ?

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    $\begingroup$ I must admit that this might be out of my area of expertise, because I've never used the word waveshaper, but is it possible that it's just another word for channel transfer function, or channel frequency response, or its time-domain equivalent impulse response? Really, out of curiosity: can you tell us which context waveshaper comes from, and maybe link me to a definition? $\endgroup$ – Marcus Müller Dec 2 '17 at 9:51
  • $\begingroup$ You could simply make a table mapping the input to the output. If you like you can then try to approximate the function implied by the table by some appropriate mathematical function. $\endgroup$ – Matt L. Dec 2 '17 at 13:55
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    $\begingroup$ @MarcusMüller: A waveshaper is just a memoryless nonlinearity applied to the input to achieve some (distortion) effect: $y=f(x)$. A simple example would be a clipping function. $\endgroup$ – Matt L. Dec 2 '17 at 13:57
  • $\begingroup$ ah, cool, @MattL. So, OP's question is, broken down, "can I derive everything about a bounded-real-to-bounded-real function from limited observation", as far as I understand. In that case, you should really post your comment as an answer (maybe with the hint that one needs to restrict one self to some parameterizable set of functions, e.g. $N$th order polynomials, linear interpolations of a table) and that with only limited quantization of both the in- and output signal, a table mapping (potentially interpolated) might be the best you can do, anyway. $\endgroup$ – Marcus Müller Dec 2 '17 at 14:55

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